Final answer:
The compound amount of $5000 at an annual interest rate of 1.11% compounded daily for one year is approximately $5056.07, and the interest earned is approximately $56.07.
Step-by-step explanation:
To find the compound amount and the interest earned from a money market account, we can use the formula for compound interest which is A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, and t is the time the money is invested for, in years.
Based on the given details, $5000 is invested at an annual interest rate of 1.11% compounded daily for one year. Converting the percentage rate to decimal, we have 1.11% = 0.0111. Since the interest is compounded daily, there are n=365 compounding periods in a year. The time t is 1 year.
The formula becomes A = $5000(1 + 0.0111/365)365*1.
Now let's calculate the compound amount A:
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- Divide the annual interest rate by the number of compounding periods: 0.0111 / 365 = 0.00003041095.
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- Add 1 to the value from step 1: 1 + 0.00003041095 = 1.00003041095.
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- Calculate the compound interest factor by raising the result of step 2 to the power of the number of compounding periods (365): (1.00003041095)365.
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- Multiply the principal amount by the result from step 3 to get the compound amount: $5000 * (1.00003041095)365.
Using a calculator, the value of (1.00003041095)365 is approximately 1.011214977, and therefore the compound amount A is approximately:
A = $5000 * 1.011214977 ≈ $5056.07
To find the interest earned, subtract the principal from the compound amount:
Interest Earned = A - P = $5056.07 - $5000 = $56.07
The compound amount is $5056.07, and the interest earned is $56.07.